Causal Effects and Experiments

GVPT399F: Power, Politics, and Data

Causes and effects

Our goal is to better understand what factors lead to certain outcomes of interest.

  • Does increasing the number of voting booths close to a potential voter make that person more likely to vote?

  • Do peace treaties signed with factionalized rebel groups more often lead to a return to conflict than those signed with a single, cohesive group?

  • Does trade between two countries make war between them less likely?

Causes and effects

These are causal statements:

  • More local voting booths \(\rightarrow\) More likely to vote

  • More factionalization \(\rightarrow\) More likely to restart conflict

  • Trade \(\rightarrow\) Less likely to go to war

How to identify causes and their effects

Proving that changes to one factor cause changes to another is very tricky!

  • Need to account for all the other factors

The efficacy of international election monitors

Do international monitors cause less election-day fraud in democratic elections?

  • Number of elections monitored by international observers exploded throughout the 2000s

  • But do monitors increase the chances the election will be free and fair?

  • In other words, are they effective?

The efficacy of international election monitors

Dr Susan Hyde set out to answer this very question. From her article (page 39):

If the presence of international observers causes a reduction in election-day fraud, the effect of observers should be visible at the subnational level by comparing polling stations that were visited by observers with those that were not visited. More specifically, if international monitoring reduces electionday fraud directly, all else held equal, the cheating parties should gain less of their ill-gotten vote share in polling stations that were visited by international monitors.

Causal relationships

Refers to the directional connection between a change in one variable and a corresponding change in another.

  • The direction matters!

  • Treatment variable: the variable causing changes to another variable.

  • Outcome variable: the variable changing as a result of changes to another variable (the treatment).

Treatment and outcome variables

We want to test whether the presence of international monitors (treatment) leads to less election day fraud (outcome).

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station

Treatment variable

At any given polling station in any given election, monitors may be: 1) present, or 2) not present.

Two different conditions:

  • Treatment: condition with treatment (monitors are present)

  • Control: condition without treatment (monitors are not present)

Outcome variable

At any given polling station in any given election, fraud may: 1) occur, or 2) not occur.

Observing our outcome

Sometimes it can be hard to observe our outcome of interest.

  • How might we see all election-day fraud?

  • How might we measure it?

Observing our outcome

Hyde’s answer: vote-share!

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station \(\rightarrow\) Lower vote-share for the cheating party

Individual causal effects

We want to know whether the treatment causes a change in our outcome of interest.

What might this look like in the real world?

  • Imagine we are looking at a specific election

  • Five polling stations

Parallel worlds

Hypothetical election

ID Monitored vote % Non-monitored vote %
1 42.87 67.93
2 57.03 59.60
3 18.43 98.52
4 50.92 78.02
5 61.59 77.07

Individual effects

The only difference between these two conditions is the presence of international monitors!

  • The difference between vote shares under these conditions is caused by the monitors.

Individual effects

ID Monitored vote % Non-monitored vote % Difference (%)
1 42.87 67.93 -25.06
2 57.03 59.60 -2.57
3 18.43 98.52 -80.09
4 50.92 78.02 -27.10
5 61.59 77.07 -15.48

No parallel worlds

Sadly for us, we cannot create parallel worlds…

What now?

ID Monitored Monitored vote % Non-monitored vote % Difference
1 0 NA 67.93 NA
2 1 57.03 NA NA
3 1 18.43 NA NA
4 0 NA 78.02 NA
5 1 61.59 NA NA

Average causal effects

We need to move away from looking at individuals and start to look for patterns in our group.

Back to our parallel worlds

ID Monitored vote % Non-monitored vote % Difference
1 42.87 67.93 -25.06
2 57.03 59.60 -2.57
3 18.43 98.52 -80.09
4 50.92 78.02 -27.10
5 61.59 77.07 -15.48

Difference of averages across all individuals

What was the average vote share received in each world?

Avg. monitored vote % Avg. non-monitored vote % Difference
46.17 76.23 -30.06

Back to reality

ID Monitored Monitored vote % Non-monitored vote % Difference
1 0 NA 67.93 NA
2 1 57.03 NA NA
3 1 18.43 NA NA
4 0 NA 78.02 NA
5 1 61.59 NA NA

Difference-of-means

What was the average vote share received in each group?

Avg. monitored vote % Avg. non-monitored vote % Difference
45.68 72.97 -27.29

How on Earth does this work so well?

Randomization!

  • Monitors were assigned to polling stations randomly (for example, with the flip of a coin)

  • This created two groups of stations that were roughly identical on average to one another prior to treatment

  • This mimics what happens when we split our world into two (creating two literally identical groups)

Our goal

We want two groups that are completely identical to one another prior to treatment.

  • This allows us to compare their outcomes after treatment and claim that the treatment caused differences in those outcomes (if any differences exist)

Our goal

Next best thing

Instead, we should try to make two groups that are as similar as possible to each other prior to treatment.

The magic of randomization

Perfectly random assignment does this very well!

Don’t take my word for it

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Our group

ID Height Weight Eye colour
1 163.78 74.41 Blue
2 170.58 65.85 Green
3 166.02 79.59 Grey
4 171.53 61.86 Brown
5 172.15 76.90 Blue
6 164.09 91.73 Green
7 158.82 80.86 Brown
8 170.03 91.88 Brown
9 175.02 77.87 Grey
10 178.45 90.49 Green
11 171.41 74.01 Green
12 168.37 83.30 Blue
13 168.15 87.85 Blue
14 166.10 93.43 Brown
15 171.57 82.85 Blue
16 161.05 70.65 Grey
17 160.18 75.65 Blue
18 159.54 86.05 Brown
19 161.62 82.55 Brown
20 165.49 69.62 Grey
21 167.46 64.25 Blue
22 166.36 78.28 Green
23 186.51 84.80 Brown
24 169.25 83.48 Grey
25 170.39 98.02 Blue
26 165.73 82.77 Brown
27 170.81 79.49 Blue
28 176.23 93.84 Grey
29 164.84 92.66 Brown
30 157.79 78.20 Green
31 182.74 82.00 Brown
32 178.83 60.37 Blue
33 179.13 80.84 Grey
34 163.60 75.25 Grey
35 173.66 81.48 Brown
36 170.36 84.61 Grey
37 168.86 85.00 Blue
38 167.28 79.94 Brown
39 181.19 70.21 Blue
40 167.24 78.67 Grey
41 168.28 101.02 Brown
42 177.86 64.07 Brown
43 164.96 94.34 Brown
44 172.15 97.22 Brown
45 162.56 86.62 Grey
46 160.63 80.51 Brown
47 161.30 56.90 Grey
48 160.91 106.68 Grey
49 174.49 68.65 Grey
50 165.60 76.27 Blue
51 165.26 80.15 Blue
52 178.85 93.54 Grey
53 173.52 94.34 Green
54 172.96 71.86 Blue
55 172.31 78.71 Grey
56 157.28 72.91 Brown
57 160.69 104.73 Blue
58 173.10 91.82 Grey
59 170.53 88.23 Grey
60 172.28 65.95 Green
61 179.21 80.94 Grey
62 176.65 77.21 Blue
63 173.68 81.33 Grey
64 167.90 81.47 Grey
65 166.93 86.84 Brown
66 184.27 69.88 Green
67 171.05 60.77 Brown
68 167.49 73.17 Brown
69 173.77 93.21 Green
70 166.44 78.07 Grey
71 170.20 74.07 Blue
72 166.24 101.94 Green
73 173.69 76.03 Green
74 179.62 72.41 Green
75 172.92 63.11 Grey
76 172.14 89.46 Green
77 162.66 72.69 Grey
78 165.43 75.95 Brown
79 175.37 86.56 Green
80 172.78 77.38 Grey
81 174.25 88.41 Brown
82 173.25 65.72 Brown
83 158.99 83.60 Green
84 174.57 113.29 Brown
85 162.76 95.24 Brown
86 161.32 92.46 Grey
87 171.01 70.59 Green
88 182.88 69.77 Green
89 169.70 75.49 Brown
90 166.00 79.31 Blue
91 173.04 77.45 Grey
92 174.02 79.06 Green
93 165.92 84.13 Brown
94 177.43 62.88 Brown
95 175.73 81.72 Brown
96 178.72 83.87 Grey
97 161.69 75.05 Green
98 163.88 64.98 Grey
99 183.71 76.58 Blue
100 181.35 84.77 Grey
101 168.97 85.89 Grey
102 158.60 104.63 Brown
103 167.58 94.40 Blue
104 164.91 77.47 Blue
105 180.59 66.70 Blue
106 171.37 80.08 Grey
107 172.67 72.09 Green
108 173.79 88.65 Grey
109 172.12 90.35 Green
110 177.23 92.71 Grey
111 162.50 72.28 Grey
112 164.53 67.57 Blue
113 167.16 78.42 Blue
114 171.64 59.48 Green
115 170.74 81.26 Brown
116 173.16 71.42 Grey
117 175.27 73.38 Green
118 165.88 76.88 Blue
119 170.11 91.98 Brown
120 167.81 72.69 Grey
121 166.64 79.89 Green
122 173.61 77.53 Grey
123 165.01 94.00 Green
124 174.55 85.45 Grey
125 168.40 86.89 Green
126 167.79 83.27 Green
127 181.07 75.26 Blue
128 178.17 71.25 Green
129 168.37 82.08 Blue
130 158.30 77.24 Grey
131 169.40 82.21 Brown
132 177.15 77.08 Grey
133 179.11 89.22 Brown
134 171.31 79.34 Green
135 171.05 86.87 Blue
136 160.21 89.59 Green
137 180.13 70.70 Green
138 172.91 86.32 Brown
139 168.72 85.30 Green
140 163.08 76.58 Green
141 165.88 83.30 Brown
142 170.66 100.31 Grey
143 169.26 78.26 Grey
144 175.03 77.29 Green
145 166.97 66.27 Brown
146 166.17 72.71 Blue
147 177.63 86.73 Brown
148 167.61 92.55 Grey
149 172.81 86.40 Grey
150 174.31 82.45 Brown
151 171.15 93.18 Blue
152 165.89 84.58 Grey
153 160.92 75.77 Grey
154 171.28 75.90 Green
155 167.32 87.26 Grey
156 171.34 75.70 Green
157 173.24 74.63 Blue
158 169.53 86.06 Blue
159 175.81 58.65 Grey
160 162.93 86.87 Grey
161 161.95 90.18 Brown
162 159.94 73.67 Grey
163 170.23 68.89 Brown
164 166.02 77.82 Brown
165 166.38 83.71 Green
166 162.10 76.76 Brown
167 164.73 77.84 Brown
168 178.31 95.98 Green
169 169.11 116.77 Grey
170 168.67 81.36 Blue
171 164.26 78.11 Blue
172 170.35 67.88 Grey
173 166.82 78.95 Green
174 175.43 83.91 Brown
175 167.83 106.39 Green
176 165.50 77.42 Green
177 169.08 80.49 Blue
178 168.04 84.63 Brown
179 172.31 71.76 Grey
180 171.68 74.84 Brown
181 162.00 78.47 Brown
182 177.73 68.71 Green
183 164.20 100.34 Green
184 174.85 96.63 Green
185 173.09 61.96 Blue
186 173.51 90.92 Blue
187 162.35 72.75 Green
188 168.50 75.10 Brown
189 178.96 88.25 Green
190 172.60 80.80 Green
191 173.45 85.57 Green
192 169.60 104.07 Grey
193 168.18 76.41 Green
194 170.38 84.17 Brown
195 171.87 55.79 Blue
196 166.34 87.18 Brown
197 179.62 84.82 Green
198 163.39 70.99 Green
199 159.52 76.36 Brown
200 170.87 80.21 Blue
201 156.99 74.33 Green
202 174.34 70.17 Brown
203 167.75 82.16 Brown
204 175.73 89.10 Blue
205 180.25 77.27 Green
206 159.68 70.89 Blue
207 156.13 84.38 Grey
208 157.87 57.02 Grey
209 171.71 69.15 Brown
210 177.01 58.10 Grey
211 153.64 95.60 Grey
212 161.33 60.01 Blue
213 170.29 89.76 Brown
214 153.79 88.42 Brown
215 175.25 69.06 Blue
216 169.64 67.22 Grey
217 169.32 100.36 Blue
218 182.49 95.12 Brown
219 171.97 93.08 Grey
220 172.15 76.61 Grey
221 166.66 61.31 Blue
222 167.36 78.28 Blue
223 164.84 93.46 Blue
224 177.34 82.48 Grey
225 167.86 100.26 Grey
226 168.98 62.97 Grey
227 178.79 91.82 Blue
228 172.25 81.57 Brown
229 171.22 94.74 Grey
230 159.62 74.51 Green
231 168.72 75.66 Brown
232 176.72 88.35 Blue
233 174.42 74.11 Green
234 173.46 88.46 Blue
235 172.99 76.62 Green
236 183.02 72.83 Brown
237 170.90 62.05 Blue
238 167.55 84.72 Brown
239 168.63 71.52 Grey
240 179.26 84.38 Blue
241 174.80 86.63 Grey
242 165.98 77.54 Green
243 167.47 74.89 Blue
244 171.36 91.33 Grey
245 174.87 90.55 Green
246 176.34 81.51 Brown
247 169.83 91.25 Green
248 181.27 82.59 Blue
249 174.46 83.72 Blue
250 166.45 79.51 Green
251 175.21 91.68 Brown
252 164.63 88.83 Blue
253 172.65 85.12 Green
254 161.44 79.05 Grey
255 160.22 78.06 Green
256 162.95 58.90 Green
257 163.92 88.55 Brown
258 171.12 91.35 Green
259 172.31 75.74 Grey
260 162.71 94.00 Brown
261 167.79 79.31 Green
262 165.45 86.52 Blue
263 158.67 80.07 Brown
264 175.89 86.58 Brown
265 177.27 73.92 Green
266 171.69 78.77 Brown
267 176.30 75.16 Brown
268 177.58 73.19 Blue
269 173.65 75.61 Grey
270 163.55 58.82 Green
271 175.36 59.86 Blue
272 166.12 92.97 Blue
273 175.43 88.66 Grey
274 175.34 90.60 Blue
275 163.33 60.55 Brown
276 167.57 92.55 Brown
277 168.64 94.24 Green
278 177.01 85.31 Green
279 157.76 96.94 Grey
280 169.40 66.92 Green
281 174.04 66.65 Grey
282 162.30 76.09 Brown
283 168.68 73.02 Grey
284 171.46 89.73 Grey
285 155.62 83.96 Brown
286 163.88 87.60 Brown
287 165.30 82.26 Grey
288 170.05 75.02 Green
289 176.00 80.03 Brown
290 169.79 90.02 Grey
291 175.48 59.95 Brown
292 169.97 84.56 Grey
293 165.47 80.25 Grey
294 172.17 86.51 Green
295 162.56 81.24 Brown
296 164.71 71.72 Brown
297 167.98 70.62 Brown
298 176.13 75.92 Brown
299 166.90 62.05 Brown
300 160.38 76.30 Brown
301 176.05 94.64 Blue
302 169.88 85.06 Grey
303 160.34 68.34 Grey
304 168.96 78.33 Grey
305 169.14 85.47 Grey
306 162.32 103.52 Grey
307 182.30 81.74 Brown
308 169.95 76.41 Brown
309 163.78 95.45 Green
310 164.81 83.50 Green
311 172.58 65.23 Green
312 160.37 56.98 Blue
313 160.34 77.51 Green
314 169.00 72.60 Blue
315 170.93 76.08 Grey
316 178.24 74.23 Blue
317 167.44 86.02 Grey
318 172.32 83.44 Brown
319 160.11 70.33 Brown
320 169.19 92.94 Blue
321 160.13 73.75 Grey
322 161.22 77.44 Green
323 165.09 65.72 Grey
324 170.76 77.62 Green
325 168.83 71.85 Brown
326 173.28 88.20 Grey
327 166.13 94.35 Blue
328 173.30 77.05 Grey
329 167.75 66.10 Blue
330 167.08 66.56 Blue
331 171.76 86.71 Brown
332 172.22 79.62 Grey
333 178.92 87.82 Green
334 173.61 77.04 Grey
335 166.65 72.24 Green
336 170.72 71.10 Grey
337 177.69 79.44 Brown
338 176.57 82.14 Green
339 174.82 57.20 Grey
340 172.50 77.92 Green
341 159.86 73.42 Blue
342 156.10 50.40 Grey
343 164.38 70.25 Grey
344 165.76 70.56 Grey
345 172.75 68.23 Green
346 175.31 73.91 Green
347 175.88 68.22 Brown
348 181.96 72.42 Green
349 159.25 88.34 Green
350 174.98 82.43 Brown
351 170.45 67.34 Green
352 174.92 89.77 Brown
353 173.09 87.01 Grey
354 161.99 69.49 Brown
355 176.87 91.45 Green
356 170.31 85.16 Brown
357 159.94 68.84 Grey
358 170.62 74.83 Grey
359 174.68 78.74 Grey
360 165.25 86.36 Green
361 171.19 76.03 Grey
362 169.62 86.50 Grey
363 161.92 80.12 Blue
364 179.98 81.82 Blue
365 166.56 80.98 Blue
366 172.88 70.35 Grey
367 171.72 77.41 Blue
368 167.28 72.54 Brown
369 154.18 94.37 Brown
370 169.32 67.50 Blue
371 173.05 87.18 Grey
372 171.71 83.69 Brown
373 167.56 88.70 Green
374 167.30 69.98 Green
375 169.08 93.31 Grey
376 182.49 73.62 Grey
377 165.36 90.18 Brown
378 171.92 72.16 Blue
379 175.99 79.17 Blue
380 158.72 76.46 Green
381 171.47 70.98 Green
382 170.04 81.50 Blue
383 161.10 85.75 Green
384 157.10 66.58 Blue
385 170.12 76.27 Blue
386 177.05 83.96 Grey
387 170.56 82.27 Blue
388 164.45 86.89 Blue
389 167.27 83.43 Grey
390 188.86 62.30 Brown
391 170.56 73.88 Blue
392 172.43 70.36 Blue
393 169.70 73.38 Grey
394 174.69 76.86 Green
395 181.03 89.21 Green
396 175.73 70.87 Green
397 168.30 88.76 Brown
398 173.32 89.62 Green
399 171.76 67.11 Grey
400 167.83 75.93 Green
401 165.53 81.77 Green
402 169.95 84.52 Blue
403 175.80 68.04 Blue
404 166.00 71.91 Green
405 180.45 87.76 Brown
406 178.68 74.53 Green
407 167.13 92.65 Blue
408 169.59 79.51 Blue
409 165.90 59.69 Grey
410 173.63 71.99 Blue
411 166.12 76.65 Grey
412 173.88 80.02 Brown
413 177.87 78.04 Grey
414 181.38 75.44 Brown
415 180.40 85.76 Grey
416 172.07 84.04 Green
417 173.92 72.82 Green
418 161.18 63.62 Grey
419 157.70 73.54 Blue
420 166.80 70.08 Brown
421 162.66 65.81 Blue
422 161.68 78.13 Green
423 175.58 81.43 Blue
424 169.82 94.81 Blue
425 168.89 74.16 Brown
426 165.93 90.96 Brown
427 164.62 80.29 Grey
428 164.95 72.86 Green
429 173.79 66.42 Green
430 173.82 73.64 Brown
431 169.33 86.71 Grey
432 168.47 68.52 Brown
433 163.12 76.82 Green
434 163.15 78.84 Brown
435 163.54 88.90 Brown
436 167.02 93.03 Grey
437 163.77 84.03 Grey
438 168.89 75.08 Green
439 166.98 83.11 Grey
440 163.83 84.04 Grey
441 169.75 83.70 Brown
442 181.35 67.88 Brown
443 177.38 82.09 Blue
444 174.42 82.26 Green
445 170.49 81.75 Grey
446 177.72 75.19 Grey
447 184.85 75.02 Green
448 177.40 70.50 Grey
449 162.63 65.06 Blue
450 163.50 92.78 Brown
451 168.78 64.76 Blue
452 171.38 104.51 Brown
453 169.35 76.09 Green
454 167.88 80.45 Blue
455 175.08 78.13 Green
456 173.69 82.04 Blue
457 168.08 77.27 Blue
458 170.48 98.85 Brown
459 164.49 66.85 Brown
460 175.68 80.29 Grey
461 159.56 85.81 Blue
462 176.62 73.56 Green
463 170.93 71.16 Green
464 175.59 96.23 Brown
465 172.10 94.54 Brown
466 178.39 91.75 Blue
467 174.84 84.82 Green
468 166.87 78.20 Blue
469 158.87 87.48 Grey
470 183.64 80.53 Grey
471 169.46 61.29 Grey
472 169.95 74.35 Blue
473 163.71 76.86 Green
474 170.46 88.57 Blue
475 165.69 76.66 Grey
476 170.84 84.45 Grey
477 175.23 80.79 Brown
478 169.10 84.88 Grey
479 178.08 78.23 Brown
480 160.25 71.02 Brown
481 164.28 78.15 Green
482 160.48 88.66 Green
483 172.45 81.87 Grey
484 166.75 73.36 Blue
485 170.84 84.59 Brown
486 167.94 95.28 Blue
487 185.18 77.09 Grey
488 180.27 87.46 Grey
489 182.95 58.84 Brown
490 172.52 91.57 Brown
491 162.55 73.46 Green
492 169.84 64.74 Grey
493 182.22 93.15 Blue
494 176.62 87.78 Blue
495 176.07 93.78 Green
496 163.66 96.00 Grey
497 164.76 73.45 Blue
498 162.16 62.03 Blue
499 164.46 72.62 Grey
500 164.46 85.36 Green
501 172.66 77.22 Grey
502 164.72 79.77 Blue
503 164.53 74.41 Blue
504 164.21 68.94 Brown
505 173.90 71.35 Brown
506 173.08 78.52 Brown
507 174.98 97.54 Green
508 163.21 82.87 Blue
509 181.52 79.56 Brown
510 167.04 94.65 Green
511 171.41 77.27 Green
512 169.29 85.21 Green
513 164.22 72.54 Blue
514 165.41 75.14 Brown
515 173.16 103.21 Grey
516 170.47 78.14 Grey
517 177.27 83.11 Blue
518 174.39 94.23 Brown
519 180.09 74.65 Green
520 170.94 92.77 Brown
521 181.94 71.66 Brown
522 178.94 88.15 Blue
523 162.73 81.44 Blue
524 170.69 77.73 Blue
525 179.62 71.02 Blue
526 172.13 78.66 Brown
527 174.08 74.45 Blue
528 181.92 71.56 Blue
529 164.18 73.49 Grey
530 173.53 82.08 Blue
531 160.14 84.64 Blue
532 172.86 79.68 Green
533 171.11 90.55 Brown
534 176.53 72.54 Grey
535 157.09 65.81 Green
536 168.33 86.89 Brown
537 167.72 82.00 Blue
538 162.70 75.75 Green
539 173.75 81.64 Brown
540 176.72 84.93 Blue
541 170.49 81.61 Green
542 176.20 70.62 Green
543 162.70 75.64 Grey
544 160.14 77.78 Grey
545 164.99 91.14 Grey
546 174.15 75.04 Grey
547 166.41 69.01 Grey
548 160.56 80.65 Blue
549 182.10 70.22 Brown
550 171.33 77.58 Blue
551 164.95 88.68 Green
552 166.30 88.66 Brown
553 169.18 98.23 Blue
554 167.69 66.31 Brown
555 159.30 83.26 Blue
556 160.34 83.82 Brown
557 171.31 91.58 Green
558 172.73 85.91 Grey
559 170.38 80.78 Blue
560 170.36 75.62 Brown
561 166.12 68.54 Green
562 167.21 81.90 Brown
563 165.31 93.51 Grey
564 171.65 86.64 Grey
565 172.62 93.18 Blue
566 163.06 76.11 Brown
567 167.67 86.63 Green
568 159.23 83.66 Brown
569 167.85 62.32 Brown
570 156.02 74.22 Green
571 177.74 58.11 Brown
572 165.61 79.17 Green
573 172.16 80.96 Brown
574 166.09 74.68 Blue
575 163.52 51.89 Green
576 179.69 76.82 Grey
577 172.21 85.97 Brown
578 169.99 66.45 Brown
579 165.92 69.16 Blue
580 166.14 91.43 Blue
581 174.38 75.75 Green
582 168.95 70.72 Blue
583 179.01 69.85 Blue
584 177.39 79.42 Brown
585 172.32 60.89 Blue
586 174.38 87.16 Brown
587 163.53 63.95 Grey
588 162.91 74.58 Blue
589 167.72 81.50 Blue
590 172.51 85.83 Blue
591 165.93 83.50 Blue
592 179.72 87.25 Grey
593 177.54 79.85 Brown
594 178.57 77.24 Blue
595 169.58 83.41 Brown
596 175.22 86.33 Brown
597 170.58 66.30 Green
598 164.77 70.29 Grey
599 179.39 78.21 Grey
600 166.69 58.40 Brown
601 170.57 88.35 Grey
602 159.59 68.78 Grey
603 178.27 65.07 Brown
604 167.78 74.72 Grey
605 169.71 71.95 Grey
606 166.35 96.21 Grey
607 168.66 72.79 Green
608 174.24 75.87 Blue
609 178.98 85.25 Blue
610 162.44 68.35 Brown
611 165.09 92.73 Brown
612 182.49 90.89 Grey
613 174.98 85.85 Green
614 178.35 79.23 Grey
615 162.77 68.82 Green
616 166.50 58.28 Blue
617 166.60 84.51 Green
618 167.74 74.44 Blue
619 168.10 79.04 Brown
620 167.70 72.36 Blue
621 169.05 71.84 Brown
622 175.71 77.82 Green
623 166.92 92.52 Grey
624 171.40 70.28 Green
625 163.86 89.66 Blue
626 175.44 88.10 Green
627 171.47 91.93 Grey
628 165.78 73.34 Blue
629 168.97 80.54 Green
630 170.81 88.80 Grey
631 173.50 86.54 Blue
632 169.86 89.35 Brown
633 158.79 84.41 Green
634 163.40 88.74 Grey
635 167.04 72.40 Green
636 167.69 75.45 Blue
637 163.36 67.83 Green
638 174.74 87.91 Blue
639 175.97 78.84 Grey
640 165.35 104.96 Blue
641 173.62 96.58 Blue
642 155.90 82.73 Brown
643 170.93 80.08 Green
644 163.56 64.60 Brown
645 162.70 74.02 Blue
646 168.54 83.33 Brown
647 176.50 64.49 Brown
648 173.72 90.36 Green
649 177.35 91.77 Green
650 182.06 82.82 Green
651 161.77 79.48 Grey
652 176.95 87.57 Blue
653 175.71 80.74 Green
654 178.88 80.38 Grey
655 176.07 80.37 Green
656 177.13 90.05 Grey
657 175.41 81.98 Brown
658 177.88 59.00 Grey
659 168.57 83.64 Grey
660 170.15 100.46 Green
661 177.67 61.22 Brown
662 171.21 81.87 Green
663 167.49 79.20 Grey
664 165.69 82.24 Green
665 169.57 83.91 Grey
666 174.98 80.03 Brown
667 162.51 90.99 Brown
668 164.44 83.23 Green
669 175.25 74.34 Blue
670 173.56 73.51 Brown
671 167.20 85.79 Green
672 174.08 75.38 Blue
673 171.63 77.51 Grey
674 169.74 82.51 Grey
675 170.26 72.92 Brown
676 171.76 79.30 Green
677 167.69 76.79 Blue
678 166.18 85.60 Grey
679 169.75 91.73 Brown
680 168.87 72.72 Green
681 158.83 78.80 Grey
682 172.18 91.13 Green
683 158.22 87.02 Green
684 174.89 74.14 Green
685 168.95 72.80 Green
686 170.95 66.03 Green
687 171.68 89.82 Green
688 174.38 58.12 Blue
689 159.84 69.40 Grey
690 173.89 80.72 Brown
691 188.30 77.06 Green
692 159.39 63.49 Blue
693 173.13 84.17 Blue
694 158.88 76.04 Green
695 164.31 70.56 Brown
696 163.19 83.83 Brown
697 164.69 86.92 Brown
698 169.05 85.97 Green
699 172.08 87.20 Green
700 167.28 81.78 Green
701 168.10 77.77 Grey
702 179.35 66.98 Grey
703 173.14 84.09 Brown
704 175.45 73.47 Grey
705 165.49 83.35 Blue
706 171.32 62.64 Grey
707 165.08 91.36 Grey
708 166.94 88.33 Blue
709 168.51 77.90 Grey
710 171.80 64.07 Grey
711 169.27 65.52 Green
712 179.79 81.76 Brown
713 168.41 68.20 Green
714 163.82 64.05 Brown
715 165.16 75.98 Grey
716 170.33 69.73 Blue
717 172.46 86.18 Brown
718 177.00 75.86 Blue
719 166.97 78.93 Brown
720 178.16 81.06 Grey
721 172.01 110.40 Grey
722 169.07 79.30 Green
723 155.60 101.02 Green
724 174.32 77.08 Blue
725 170.87 84.35 Blue
726 170.74 64.47 Brown
727 164.65 77.07 Green
728 161.12 86.85 Blue
729 163.97 99.37 Green
730 175.22 71.54 Brown
731 171.85 86.71 Grey
732 170.54 79.05 Green
733 173.96 98.89 Grey
734 178.99 74.09 Grey
735 175.92 99.24 Grey
736 172.69 82.84 Green
737 175.54 69.94 Brown
738 166.62 90.57 Blue
739 181.53 92.39 Grey
740 177.85 78.93 Green
741 162.37 80.50 Blue
742 165.50 98.43 Green
743 176.27 84.84 Brown
744 164.03 89.25 Brown
745 161.26 82.52 Brown
746 167.59 71.98 Blue
747 166.67 75.30 Brown
748 171.85 89.21 Brown
749 169.35 81.13 Green
750 164.87 85.42 Green
751 166.99 71.90 Blue
752 186.62 62.03 Blue
753 168.51 76.56 Blue
754 166.29 77.20 Blue
755 177.38 91.71 Green
756 166.82 80.08 Grey
757 175.70 77.16 Green
758 172.53 93.36 Brown
759 170.03 80.04 Blue
760 166.92 83.79 Blue
761 162.24 106.70 Blue
762 159.92 89.30 Grey
763 173.75 87.83 Grey
764 168.42 73.74 Green
765 165.40 89.65 Brown
766 178.01 57.72 Brown
767 186.72 97.41 Brown
768 165.81 79.06 Grey
769 175.23 84.75 Grey
770 162.83 74.12 Green
771 176.22 58.95 Blue
772 167.14 78.42 Brown
773 169.12 81.93 Blue
774 173.01 90.52 Green
775 168.90 77.67 Blue
776 166.33 76.26 Blue
777 176.14 97.18 Brown
778 154.47 86.45 Blue
779 166.31 75.06 Grey
780 171.26 93.70 Brown
781 165.47 71.88 Grey
782 163.28 82.55 Blue
783 178.57 104.71 Green
784 181.04 91.82 Grey
785 171.47 68.21 Blue
786 161.16 75.47 Grey
787 163.40 94.78 Grey
788 167.33 58.61 Green
789 164.35 59.99 Blue
790 171.62 86.46 Brown
791 181.28 61.32 Blue
792 174.92 87.11 Grey
793 169.18 76.40 Blue
794 171.77 90.57 Blue
795 163.38 84.10 Blue
796 161.01 80.07 Grey
797 164.67 79.41 Brown
798 145.77 75.57 Green
799 168.85 80.74 Brown
800 178.09 64.67 Blue
801 166.56 64.92 Green
802 169.67 62.40 Blue
803 168.91 75.24 Brown
804 175.70 86.22 Brown
805 169.59 75.04 Green
806 170.56 74.68 Grey
807 165.75 67.47 Blue
808 177.28 97.66 Green
809 166.19 66.06 Brown
810 161.09 85.11 Brown
811 175.29 73.76 Blue
812 167.81 62.30 Blue
813 149.02 71.32 Brown
814 175.20 83.20 Brown
815 162.19 87.18 Grey
816 162.86 58.45 Blue
817 174.49 87.36 Grey
818 166.83 82.74 Grey
819 168.23 81.04 Green
820 155.84 85.30 Grey
821 177.69 72.09 Grey
822 165.64 64.78 Blue
823 175.61 57.63 Green
824 168.65 65.50 Green
825 168.19 73.50 Brown
826 160.97 69.17 Brown
827 172.59 75.15 Grey
828 164.57 76.37 Grey
829 161.52 102.10 Blue
830 167.60 75.63 Green
831 159.57 82.57 Grey
832 181.38 67.67 Grey
833 174.37 83.58 Brown
834 166.84 101.06 Grey
835 168.08 78.70 Grey
836 170.06 84.93 Grey
837 164.15 81.69 Grey
838 166.47 79.66 Blue
839 171.32 93.22 Blue
840 165.32 61.17 Grey
841 163.05 90.96 Blue
842 170.06 82.31 Green
843 166.00 94.32 Grey
844 176.88 69.82 Green
845 171.61 71.17 Green
846 170.56 77.13 Blue
847 167.41 71.44 Brown
848 180.97 70.14 Green
849 163.05 81.80 Brown
850 173.24 76.54 Green
851 171.95 91.83 Grey
852 172.58 69.53 Grey
853 169.82 79.90 Grey
854 168.76 70.36 Brown
855 165.57 66.94 Brown
856 165.64 86.68 Grey
857 172.65 81.79 Grey
858 174.23 93.83 Grey
859 170.98 95.12 Green
860 167.96 100.21 Grey
861 162.46 73.96 Green
862 172.17 69.95 Blue
863 171.55 85.18 Blue
864 170.75 80.21 Grey
865 171.45 82.45 Blue
866 168.86 63.56 Brown
867 170.94 72.61 Grey
868 169.32 71.10 Brown
869 168.43 86.28 Brown
870 178.98 79.95 Green
871 162.09 83.66 Green
872 165.96 79.63 Grey
873 176.35 91.04 Grey
874 170.44 77.09 Grey
875 182.15 62.12 Green
876 169.59 91.32 Brown
877 167.78 88.51 Brown
878 176.23 89.50 Green
879 175.55 77.28 Blue
880 174.00 87.61 Grey
881 171.90 84.87 Grey
882 171.55 88.03 Grey
883 175.78 74.56 Green
884 165.56 95.41 Grey
885 168.70 83.46 Grey
886 178.40 79.58 Grey
887 165.73 63.80 Grey
888 169.92 69.94 Brown
889 172.25 87.50 Brown
890 167.36 83.59 Green
891 170.87 82.55 Blue
892 171.85 99.37 Blue
893 165.09 85.44 Brown
894 169.12 85.63 Grey
895 173.59 96.43 Green
896 166.72 84.92 Brown
897 167.42 82.32 Blue
898 175.20 91.37 Green
899 174.29 72.11 Blue
900 159.74 82.42 Grey
901 161.16 94.03 Brown
902 168.88 77.38 Brown
903 172.94 84.08 Blue
904 168.29 66.75 Brown
905 163.90 96.48 Blue
906 172.87 76.86 Green
907 165.00 76.11 Green
908 176.67 72.49 Brown
909 173.21 67.43 Blue
910 178.69 70.71 Grey
911 175.37 80.74 Blue
912 170.44 75.34 Brown
913 183.85 83.16 Grey
914 165.54 70.05 Brown
915 165.38 70.01 Brown
916 174.04 84.48 Grey
917 176.54 74.08 Blue
918 166.04 87.86 Blue
919 183.19 86.52 Blue
920 176.42 86.11 Blue
921 168.77 74.25 Grey
922 169.63 76.10 Green
923 167.36 95.42 Grey
924 168.86 87.50 Green
925 170.80 82.59 Grey
926 167.38 85.27 Grey
927 168.57 84.82 Brown
928 168.52 67.63 Brown
929 154.96 60.19 Grey
930 165.01 70.43 Grey
931 174.22 72.01 Green
932 163.02 73.59 Brown
933 168.62 92.42 Blue
934 170.49 70.01 Green
935 163.18 72.90 Green
936 171.04 82.76 Green
937 177.62 82.10 Grey
938 177.04 96.87 Grey
939 168.86 78.12 Grey
940 170.55 75.40 Brown
941 166.63 77.53 Brown
942 174.62 84.61 Brown
943 169.67 86.01 Grey
944 173.14 65.30 Brown
945 168.91 92.88 Grey
946 175.72 100.47 Blue
947 168.86 87.00 Blue
948 163.16 64.77 Green
949 175.90 96.98 Grey
950 172.91 82.94 Brown
951 168.12 83.14 Green
952 179.05 70.89 Grey
953 171.53 78.21 Green
954 166.33 79.46 Brown
955 167.23 99.24 Green
956 167.55 70.53 Grey
957 172.56 77.99 Green
958 165.40 93.89 Green
959 167.56 108.18 Brown
960 179.43 86.27 Grey
961 168.12 102.66 Green
962 178.10 81.58 Green
963 159.26 91.27 Blue
964 177.55 73.36 Grey
965 174.34 83.73 Grey
966 162.21 69.50 Brown
967 165.94 89.35 Green
968 175.50 85.62 Green
969 174.67 66.59 Blue
970 183.81 72.48 Blue
971 177.74 71.53 Brown
972 177.63 83.62 Grey
973 177.25 89.06 Brown
974 168.01 77.73 Brown
975 164.39 87.42 Grey
976 159.58 83.05 Blue
977 169.57 90.05 Brown
978 171.71 72.49 Green
979 174.01 86.33 Green
980 169.70 88.73 Brown
981 171.17 55.67 Grey
982 183.18 85.62 Blue
983 167.56 87.83 Green
984 168.40 72.80 Brown
985 172.76 64.19 Brown
986 165.22 79.76 Brown
987 181.94 81.98 Green
988 165.45 77.13 Blue
989 171.64 81.98 Brown
990 165.18 82.55 Blue
991 180.16 74.26 Grey
992 166.35 87.20 Brown
993 176.88 105.53 Brown
994 171.26 75.40 Blue
995 166.23 69.38 Brown
996 164.65 79.00 Green
997 163.37 50.55 Green
998 175.24 63.54 Blue
999 168.83 72.38 Green
1000 169.09 76.97 Blue

Random assignment

I’m now going to flip (an imaginary, computer-generated) coin for each of these 1,000 individuals to assigned them to group A or B:

ID Height Weight Eye colour Group
1 163.78 74.41 Blue A
2 170.58 65.85 Green A
3 166.02 79.59 Grey B
4 171.53 61.86 Brown A
5 172.15 76.90 Blue A
6 164.09 91.73 Green A
7 158.82 80.86 Brown B
8 170.03 91.88 Brown A
9 175.02 77.87 Grey B
10 178.45 90.49 Green A
11 171.41 74.01 Green A
12 168.37 83.30 Blue A
13 168.15 87.85 Blue B
14 166.10 93.43 Brown A
15 171.57 82.85 Blue A
16 161.05 70.65 Grey B
17 160.18 75.65 Blue B
18 159.54 86.05 Brown B
19 161.62 82.55 Brown B
20 165.49 69.62 Grey A
21 167.46 64.25 Blue A
22 166.36 78.28 Green A
23 186.51 84.80 Brown A
24 169.25 83.48 Grey A
25 170.39 98.02 Blue A
26 165.73 82.77 Brown A
27 170.81 79.49 Blue A
28 176.23 93.84 Grey B
29 164.84 92.66 Brown B
30 157.79 78.20 Green A
31 182.74 82.00 Brown B
32 178.83 60.37 Blue B
33 179.13 80.84 Grey A
34 163.60 75.25 Grey A
35 173.66 81.48 Brown A
36 170.36 84.61 Grey B
37 168.86 85.00 Blue B
38 167.28 79.94 Brown A
39 181.19 70.21 Blue B
40 167.24 78.67 Grey B
41 168.28 101.02 Brown A
42 177.86 64.07 Brown B
43 164.96 94.34 Brown A
44 172.15 97.22 Brown B
45 162.56 86.62 Grey B
46 160.63 80.51 Brown B
47 161.30 56.90 Grey B
48 160.91 106.68 Grey B
49 174.49 68.65 Grey B
50 165.60 76.27 Blue A
51 165.26 80.15 Blue B
52 178.85 93.54 Grey A
53 173.52 94.34 Green A
54 172.96 71.86 Blue B
55 172.31 78.71 Grey B
56 157.28 72.91 Brown B
57 160.69 104.73 Blue B
58 173.10 91.82 Grey A
59 170.53 88.23 Grey B
60 172.28 65.95 Green B
61 179.21 80.94 Grey B
62 176.65 77.21 Blue B
63 173.68 81.33 Grey B
64 167.90 81.47 Grey A
65 166.93 86.84 Brown A
66 184.27 69.88 Green A
67 171.05 60.77 Brown B
68 167.49 73.17 Brown A
69 173.77 93.21 Green A
70 166.44 78.07 Grey A
71 170.20 74.07 Blue B
72 166.24 101.94 Green B
73 173.69 76.03 Green B
74 179.62 72.41 Green A
75 172.92 63.11 Grey A
76 172.14 89.46 Green B
77 162.66 72.69 Grey A
78 165.43 75.95 Brown A
79 175.37 86.56 Green B
80 172.78 77.38 Grey B
81 174.25 88.41 Brown B
82 173.25 65.72 Brown B
83 158.99 83.60 Green B
84 174.57 113.29 Brown A
85 162.76 95.24 Brown B
86 161.32 92.46 Grey A
87 171.01 70.59 Green B
88 182.88 69.77 Green A
89 169.70 75.49 Brown A
90 166.00 79.31 Blue B
91 173.04 77.45 Grey A
92 174.02 79.06 Green B
93 165.92 84.13 Brown A
94 177.43 62.88 Brown A
95 175.73 81.72 Brown A
96 178.72 83.87 Grey B
97 161.69 75.05 Green B
98 163.88 64.98 Grey A
99 183.71 76.58 Blue B
100 181.35 84.77 Grey A
101 168.97 85.89 Grey B
102 158.60 104.63 Brown B
103 167.58 94.40 Blue B
104 164.91 77.47 Blue B
105 180.59 66.70 Blue B
106 171.37 80.08 Grey B
107 172.67 72.09 Green B
108 173.79 88.65 Grey A
109 172.12 90.35 Green B
110 177.23 92.71 Grey A
111 162.50 72.28 Grey B
112 164.53 67.57 Blue A
113 167.16 78.42 Blue A
114 171.64 59.48 Green B
115 170.74 81.26 Brown A
116 173.16 71.42 Grey B
117 175.27 73.38 Green B
118 165.88 76.88 Blue A
119 170.11 91.98 Brown A
120 167.81 72.69 Grey A
121 166.64 79.89 Green A
122 173.61 77.53 Grey B
123 165.01 94.00 Green B
124 174.55 85.45 Grey A
125 168.40 86.89 Green A
126 167.79 83.27 Green A
127 181.07 75.26 Blue B
128 178.17 71.25 Green B
129 168.37 82.08 Blue B
130 158.30 77.24 Grey A
131 169.40 82.21 Brown A
132 177.15 77.08 Grey A
133 179.11 89.22 Brown A
134 171.31 79.34 Green B
135 171.05 86.87 Blue A
136 160.21 89.59 Green A
137 180.13 70.70 Green A
138 172.91 86.32 Brown B
139 168.72 85.30 Green A
140 163.08 76.58 Green B
141 165.88 83.30 Brown B
142 170.66 100.31 Grey B
143 169.26 78.26 Grey A
144 175.03 77.29 Green B
145 166.97 66.27 Brown A
146 166.17 72.71 Blue B
147 177.63 86.73 Brown A
148 167.61 92.55 Grey B
149 172.81 86.40 Grey A
150 174.31 82.45 Brown A
151 171.15 93.18 Blue A
152 165.89 84.58 Grey A
153 160.92 75.77 Grey B
154 171.28 75.90 Green B
155 167.32 87.26 Grey A
156 171.34 75.70 Green B
157 173.24 74.63 Blue B
158 169.53 86.06 Blue B
159 175.81 58.65 Grey B
160 162.93 86.87 Grey B
161 161.95 90.18 Brown A
162 159.94 73.67 Grey B
163 170.23 68.89 Brown B
164 166.02 77.82 Brown B
165 166.38 83.71 Green A
166 162.10 76.76 Brown B
167 164.73 77.84 Brown B
168 178.31 95.98 Green A
169 169.11 116.77 Grey A
170 168.67 81.36 Blue A
171 164.26 78.11 Blue A
172 170.35 67.88 Grey A
173 166.82 78.95 Green A
174 175.43 83.91 Brown A
175 167.83 106.39 Green B
176 165.50 77.42 Green B
177 169.08 80.49 Blue B
178 168.04 84.63 Brown A
179 172.31 71.76 Grey A
180 171.68 74.84 Brown A
181 162.00 78.47 Brown B
182 177.73 68.71 Green B
183 164.20 100.34 Green A
184 174.85 96.63 Green A
185 173.09 61.96 Blue B
186 173.51 90.92 Blue A
187 162.35 72.75 Green A
188 168.50 75.10 Brown B
189 178.96 88.25 Green A
190 172.60 80.80 Green B
191 173.45 85.57 Green B
192 169.60 104.07 Grey A
193 168.18 76.41 Green B
194 170.38 84.17 Brown B
195 171.87 55.79 Blue A
196 166.34 87.18 Brown A
197 179.62 84.82 Green A
198 163.39 70.99 Green B
199 159.52 76.36 Brown B
200 170.87 80.21 Blue A
201 156.99 74.33 Green A
202 174.34 70.17 Brown A
203 167.75 82.16 Brown B
204 175.73 89.10 Blue A
205 180.25 77.27 Green A
206 159.68 70.89 Blue B
207 156.13 84.38 Grey B
208 157.87 57.02 Grey B
209 171.71 69.15 Brown B
210 177.01 58.10 Grey A
211 153.64 95.60 Grey B
212 161.33 60.01 Blue A
213 170.29 89.76 Brown B
214 153.79 88.42 Brown B
215 175.25 69.06 Blue A
216 169.64 67.22 Grey B
217 169.32 100.36 Blue B
218 182.49 95.12 Brown A
219 171.97 93.08 Grey B
220 172.15 76.61 Grey B
221 166.66 61.31 Blue B
222 167.36 78.28 Blue A
223 164.84 93.46 Blue A
224 177.34 82.48 Grey B
225 167.86 100.26 Grey A
226 168.98 62.97 Grey A
227 178.79 91.82 Blue B
228 172.25 81.57 Brown A
229 171.22 94.74 Grey A
230 159.62 74.51 Green A
231 168.72 75.66 Brown B
232 176.72 88.35 Blue B
233 174.42 74.11 Green B
234 173.46 88.46 Blue B
235 172.99 76.62 Green B
236 183.02 72.83 Brown A
237 170.90 62.05 Blue B
238 167.55 84.72 Brown A
239 168.63 71.52 Grey A
240 179.26 84.38 Blue B
241 174.80 86.63 Grey B
242 165.98 77.54 Green A
243 167.47 74.89 Blue B
244 171.36 91.33 Grey A
245 174.87 90.55 Green B
246 176.34 81.51 Brown B
247 169.83 91.25 Green A
248 181.27 82.59 Blue A
249 174.46 83.72 Blue B
250 166.45 79.51 Green A
251 175.21 91.68 Brown A
252 164.63 88.83 Blue A
253 172.65 85.12 Green A
254 161.44 79.05 Grey A
255 160.22 78.06 Green A
256 162.95 58.90 Green A
257 163.92 88.55 Brown B
258 171.12 91.35 Green B
259 172.31 75.74 Grey A
260 162.71 94.00 Brown B
261 167.79 79.31 Green A
262 165.45 86.52 Blue A
263 158.67 80.07 Brown A
264 175.89 86.58 Brown B
265 177.27 73.92 Green A
266 171.69 78.77 Brown B
267 176.30 75.16 Brown A
268 177.58 73.19 Blue B
269 173.65 75.61 Grey A
270 163.55 58.82 Green A
271 175.36 59.86 Blue A
272 166.12 92.97 Blue B
273 175.43 88.66 Grey A
274 175.34 90.60 Blue A
275 163.33 60.55 Brown B
276 167.57 92.55 Brown B
277 168.64 94.24 Green B
278 177.01 85.31 Green A
279 157.76 96.94 Grey B
280 169.40 66.92 Green A
281 174.04 66.65 Grey B
282 162.30 76.09 Brown A
283 168.68 73.02 Grey A
284 171.46 89.73 Grey A
285 155.62 83.96 Brown A
286 163.88 87.60 Brown A
287 165.30 82.26 Grey A
288 170.05 75.02 Green B
289 176.00 80.03 Brown A
290 169.79 90.02 Grey B
291 175.48 59.95 Brown B
292 169.97 84.56 Grey B
293 165.47 80.25 Grey A
294 172.17 86.51 Green B
295 162.56 81.24 Brown A
296 164.71 71.72 Brown B
297 167.98 70.62 Brown B
298 176.13 75.92 Brown A
299 166.90 62.05 Brown A
300 160.38 76.30 Brown A
301 176.05 94.64 Blue B
302 169.88 85.06 Grey A
303 160.34 68.34 Grey B
304 168.96 78.33 Grey B
305 169.14 85.47 Grey B
306 162.32 103.52 Grey B
307 182.30 81.74 Brown B
308 169.95 76.41 Brown B
309 163.78 95.45 Green A
310 164.81 83.50 Green A
311 172.58 65.23 Green B
312 160.37 56.98 Blue A
313 160.34 77.51 Green A
314 169.00 72.60 Blue B
315 170.93 76.08 Grey A
316 178.24 74.23 Blue B
317 167.44 86.02 Grey A
318 172.32 83.44 Brown A
319 160.11 70.33 Brown B
320 169.19 92.94 Blue B
321 160.13 73.75 Grey B
322 161.22 77.44 Green A
323 165.09 65.72 Grey B
324 170.76 77.62 Green A
325 168.83 71.85 Brown A
326 173.28 88.20 Grey B
327 166.13 94.35 Blue A
328 173.30 77.05 Grey A
329 167.75 66.10 Blue A
330 167.08 66.56 Blue B
331 171.76 86.71 Brown B
332 172.22 79.62 Grey B
333 178.92 87.82 Green B
334 173.61 77.04 Grey A
335 166.65 72.24 Green B
336 170.72 71.10 Grey B
337 177.69 79.44 Brown A
338 176.57 82.14 Green A
339 174.82 57.20 Grey B
340 172.50 77.92 Green A
341 159.86 73.42 Blue A
342 156.10 50.40 Grey B
343 164.38 70.25 Grey B
344 165.76 70.56 Grey A
345 172.75 68.23 Green B
346 175.31 73.91 Green B
347 175.88 68.22 Brown B
348 181.96 72.42 Green A
349 159.25 88.34 Green B
350 174.98 82.43 Brown B
351 170.45 67.34 Green A
352 174.92 89.77 Brown A
353 173.09 87.01 Grey A
354 161.99 69.49 Brown B
355 176.87 91.45 Green A
356 170.31 85.16 Brown A
357 159.94 68.84 Grey A
358 170.62 74.83 Grey A
359 174.68 78.74 Grey A
360 165.25 86.36 Green B
361 171.19 76.03 Grey A
362 169.62 86.50 Grey A
363 161.92 80.12 Blue B
364 179.98 81.82 Blue B
365 166.56 80.98 Blue A
366 172.88 70.35 Grey B
367 171.72 77.41 Blue A
368 167.28 72.54 Brown B
369 154.18 94.37 Brown B
370 169.32 67.50 Blue B
371 173.05 87.18 Grey A
372 171.71 83.69 Brown B
373 167.56 88.70 Green B
374 167.30 69.98 Green B
375 169.08 93.31 Grey B
376 182.49 73.62 Grey B
377 165.36 90.18 Brown A
378 171.92 72.16 Blue A
379 175.99 79.17 Blue A
380 158.72 76.46 Green A
381 171.47 70.98 Green A
382 170.04 81.50 Blue A
383 161.10 85.75 Green A
384 157.10 66.58 Blue B
385 170.12 76.27 Blue A
386 177.05 83.96 Grey A
387 170.56 82.27 Blue B
388 164.45 86.89 Blue B
389 167.27 83.43 Grey A
390 188.86 62.30 Brown B
391 170.56 73.88 Blue B
392 172.43 70.36 Blue A
393 169.70 73.38 Grey A
394 174.69 76.86 Green B
395 181.03 89.21 Green A
396 175.73 70.87 Green B
397 168.30 88.76 Brown A
398 173.32 89.62 Green A
399 171.76 67.11 Grey B
400 167.83 75.93 Green B
401 165.53 81.77 Green B
402 169.95 84.52 Blue B
403 175.80 68.04 Blue A
404 166.00 71.91 Green A
405 180.45 87.76 Brown A
406 178.68 74.53 Green A
407 167.13 92.65 Blue B
408 169.59 79.51 Blue A
409 165.90 59.69 Grey A
410 173.63 71.99 Blue B
411 166.12 76.65 Grey A
412 173.88 80.02 Brown A
413 177.87 78.04 Grey B
414 181.38 75.44 Brown B
415 180.40 85.76 Grey B
416 172.07 84.04 Green A
417 173.92 72.82 Green B
418 161.18 63.62 Grey A
419 157.70 73.54 Blue B
420 166.80 70.08 Brown A
421 162.66 65.81 Blue A
422 161.68 78.13 Green B
423 175.58 81.43 Blue A
424 169.82 94.81 Blue A
425 168.89 74.16 Brown B
426 165.93 90.96 Brown A
427 164.62 80.29 Grey B
428 164.95 72.86 Green A
429 173.79 66.42 Green B
430 173.82 73.64 Brown A
431 169.33 86.71 Grey A
432 168.47 68.52 Brown A
433 163.12 76.82 Green B
434 163.15 78.84 Brown A
435 163.54 88.90 Brown A
436 167.02 93.03 Grey A
437 163.77 84.03 Grey B
438 168.89 75.08 Green B
439 166.98 83.11 Grey B
440 163.83 84.04 Grey B
441 169.75 83.70 Brown A
442 181.35 67.88 Brown B
443 177.38 82.09 Blue A
444 174.42 82.26 Green A
445 170.49 81.75 Grey B
446 177.72 75.19 Grey B
447 184.85 75.02 Green B
448 177.40 70.50 Grey B
449 162.63 65.06 Blue A
450 163.50 92.78 Brown B
451 168.78 64.76 Blue A
452 171.38 104.51 Brown A
453 169.35 76.09 Green A
454 167.88 80.45 Blue A
455 175.08 78.13 Green A
456 173.69 82.04 Blue A
457 168.08 77.27 Blue A
458 170.48 98.85 Brown A
459 164.49 66.85 Brown B
460 175.68 80.29 Grey A
461 159.56 85.81 Blue B
462 176.62 73.56 Green B
463 170.93 71.16 Green B
464 175.59 96.23 Brown A
465 172.10 94.54 Brown B
466 178.39 91.75 Blue A
467 174.84 84.82 Green A
468 166.87 78.20 Blue B
469 158.87 87.48 Grey B
470 183.64 80.53 Grey B
471 169.46 61.29 Grey B
472 169.95 74.35 Blue B
473 163.71 76.86 Green B
474 170.46 88.57 Blue B
475 165.69 76.66 Grey A
476 170.84 84.45 Grey A
477 175.23 80.79 Brown B
478 169.10 84.88 Grey A
479 178.08 78.23 Brown A
480 160.25 71.02 Brown B
481 164.28 78.15 Green A
482 160.48 88.66 Green A
483 172.45 81.87 Grey A
484 166.75 73.36 Blue B
485 170.84 84.59 Brown B
486 167.94 95.28 Blue A
487 185.18 77.09 Grey A
488 180.27 87.46 Grey A
489 182.95 58.84 Brown B
490 172.52 91.57 Brown A
491 162.55 73.46 Green B
492 169.84 64.74 Grey B
493 182.22 93.15 Blue A
494 176.62 87.78 Blue A
495 176.07 93.78 Green B
496 163.66 96.00 Grey B
497 164.76 73.45 Blue A
498 162.16 62.03 Blue A
499 164.46 72.62 Grey B
500 164.46 85.36 Green A
501 172.66 77.22 Grey B
502 164.72 79.77 Blue A
503 164.53 74.41 Blue A
504 164.21 68.94 Brown B
505 173.90 71.35 Brown B
506 173.08 78.52 Brown A
507 174.98 97.54 Green A
508 163.21 82.87 Blue B
509 181.52 79.56 Brown A
510 167.04 94.65 Green B
511 171.41 77.27 Green B
512 169.29 85.21 Green A
513 164.22 72.54 Blue B
514 165.41 75.14 Brown B
515 173.16 103.21 Grey B
516 170.47 78.14 Grey B
517 177.27 83.11 Blue B
518 174.39 94.23 Brown B
519 180.09 74.65 Green A
520 170.94 92.77 Brown B
521 181.94 71.66 Brown A
522 178.94 88.15 Blue B
523 162.73 81.44 Blue A
524 170.69 77.73 Blue B
525 179.62 71.02 Blue B
526 172.13 78.66 Brown A
527 174.08 74.45 Blue A
528 181.92 71.56 Blue A
529 164.18 73.49 Grey B
530 173.53 82.08 Blue B
531 160.14 84.64 Blue A
532 172.86 79.68 Green B
533 171.11 90.55 Brown A
534 176.53 72.54 Grey A
535 157.09 65.81 Green B
536 168.33 86.89 Brown B
537 167.72 82.00 Blue A
538 162.70 75.75 Green B
539 173.75 81.64 Brown A
540 176.72 84.93 Blue A
541 170.49 81.61 Green B
542 176.20 70.62 Green A
543 162.70 75.64 Grey A
544 160.14 77.78 Grey B
545 164.99 91.14 Grey A
546 174.15 75.04 Grey A
547 166.41 69.01 Grey B
548 160.56 80.65 Blue B
549 182.10 70.22 Brown B
550 171.33 77.58 Blue A
551 164.95 88.68 Green B
552 166.30 88.66 Brown B
553 169.18 98.23 Blue B
554 167.69 66.31 Brown A
555 159.30 83.26 Blue A
556 160.34 83.82 Brown B
557 171.31 91.58 Green B
558 172.73 85.91 Grey B
559 170.38 80.78 Blue B
560 170.36 75.62 Brown B
561 166.12 68.54 Green B
562 167.21 81.90 Brown A
563 165.31 93.51 Grey B
564 171.65 86.64 Grey B
565 172.62 93.18 Blue A
566 163.06 76.11 Brown B
567 167.67 86.63 Green A
568 159.23 83.66 Brown A
569 167.85 62.32 Brown B
570 156.02 74.22 Green B
571 177.74 58.11 Brown B
572 165.61 79.17 Green A
573 172.16 80.96 Brown A
574 166.09 74.68 Blue B
575 163.52 51.89 Green A
576 179.69 76.82 Grey A
577 172.21 85.97 Brown A
578 169.99 66.45 Brown A
579 165.92 69.16 Blue A
580 166.14 91.43 Blue B
581 174.38 75.75 Green B
582 168.95 70.72 Blue A
583 179.01 69.85 Blue A
584 177.39 79.42 Brown A
585 172.32 60.89 Blue B
586 174.38 87.16 Brown A
587 163.53 63.95 Grey B
588 162.91 74.58 Blue A
589 167.72 81.50 Blue A
590 172.51 85.83 Blue A
591 165.93 83.50 Blue A
592 179.72 87.25 Grey B
593 177.54 79.85 Brown A
594 178.57 77.24 Blue A
595 169.58 83.41 Brown A
596 175.22 86.33 Brown B
597 170.58 66.30 Green B
598 164.77 70.29 Grey A
599 179.39 78.21 Grey B
600 166.69 58.40 Brown B
601 170.57 88.35 Grey A
602 159.59 68.78 Grey A
603 178.27 65.07 Brown B
604 167.78 74.72 Grey B
605 169.71 71.95 Grey A
606 166.35 96.21 Grey A
607 168.66 72.79 Green A
608 174.24 75.87 Blue B
609 178.98 85.25 Blue B
610 162.44 68.35 Brown B
611 165.09 92.73 Brown A
612 182.49 90.89 Grey B
613 174.98 85.85 Green A
614 178.35 79.23 Grey A
615 162.77 68.82 Green B
616 166.50 58.28 Blue B
617 166.60 84.51 Green B
618 167.74 74.44 Blue B
619 168.10 79.04 Brown B
620 167.70 72.36 Blue A
621 169.05 71.84 Brown B
622 175.71 77.82 Green A
623 166.92 92.52 Grey B
624 171.40 70.28 Green B
625 163.86 89.66 Blue A
626 175.44 88.10 Green A
627 171.47 91.93 Grey A
628 165.78 73.34 Blue A
629 168.97 80.54 Green A
630 170.81 88.80 Grey B
631 173.50 86.54 Blue B
632 169.86 89.35 Brown B
633 158.79 84.41 Green B
634 163.40 88.74 Grey B
635 167.04 72.40 Green A
636 167.69 75.45 Blue A
637 163.36 67.83 Green A
638 174.74 87.91 Blue A
639 175.97 78.84 Grey B
640 165.35 104.96 Blue A
641 173.62 96.58 Blue B
642 155.90 82.73 Brown B
643 170.93 80.08 Green A
644 163.56 64.60 Brown A
645 162.70 74.02 Blue A
646 168.54 83.33 Brown B
647 176.50 64.49 Brown A
648 173.72 90.36 Green B
649 177.35 91.77 Green A
650 182.06 82.82 Green A
651 161.77 79.48 Grey B
652 176.95 87.57 Blue B
653 175.71 80.74 Green B
654 178.88 80.38 Grey B
655 176.07 80.37 Green B
656 177.13 90.05 Grey B
657 175.41 81.98 Brown B
658 177.88 59.00 Grey B
659 168.57 83.64 Grey A
660 170.15 100.46 Green B
661 177.67 61.22 Brown B
662 171.21 81.87 Green A
663 167.49 79.20 Grey A
664 165.69 82.24 Green A
665 169.57 83.91 Grey A
666 174.98 80.03 Brown A
667 162.51 90.99 Brown B
668 164.44 83.23 Green A
669 175.25 74.34 Blue A
670 173.56 73.51 Brown B
671 167.20 85.79 Green B
672 174.08 75.38 Blue B
673 171.63 77.51 Grey B
674 169.74 82.51 Grey B
675 170.26 72.92 Brown A
676 171.76 79.30 Green A
677 167.69 76.79 Blue B
678 166.18 85.60 Grey B
679 169.75 91.73 Brown B
680 168.87 72.72 Green B
681 158.83 78.80 Grey A
682 172.18 91.13 Green B
683 158.22 87.02 Green B
684 174.89 74.14 Green B
685 168.95 72.80 Green B
686 170.95 66.03 Green B
687 171.68 89.82 Green A
688 174.38 58.12 Blue A
689 159.84 69.40 Grey B
690 173.89 80.72 Brown A
691 188.30 77.06 Green B
692 159.39 63.49 Blue A
693 173.13 84.17 Blue B
694 158.88 76.04 Green B
695 164.31 70.56 Brown B
696 163.19 83.83 Brown A
697 164.69 86.92 Brown B
698 169.05 85.97 Green A
699 172.08 87.20 Green B
700 167.28 81.78 Green B
701 168.10 77.77 Grey A
702 179.35 66.98 Grey A
703 173.14 84.09 Brown A
704 175.45 73.47 Grey B
705 165.49 83.35 Blue B
706 171.32 62.64 Grey A
707 165.08 91.36 Grey B
708 166.94 88.33 Blue B
709 168.51 77.90 Grey A
710 171.80 64.07 Grey A
711 169.27 65.52 Green B
712 179.79 81.76 Brown A
713 168.41 68.20 Green A
714 163.82 64.05 Brown A
715 165.16 75.98 Grey A
716 170.33 69.73 Blue A
717 172.46 86.18 Brown B
718 177.00 75.86 Blue B
719 166.97 78.93 Brown B
720 178.16 81.06 Grey A
721 172.01 110.40 Grey A
722 169.07 79.30 Green A
723 155.60 101.02 Green B
724 174.32 77.08 Blue A
725 170.87 84.35 Blue A
726 170.74 64.47 Brown B
727 164.65 77.07 Green A
728 161.12 86.85 Blue B
729 163.97 99.37 Green A
730 175.22 71.54 Brown A
731 171.85 86.71 Grey A
732 170.54 79.05 Green A
733 173.96 98.89 Grey B
734 178.99 74.09 Grey B
735 175.92 99.24 Grey B
736 172.69 82.84 Green B
737 175.54 69.94 Brown A
738 166.62 90.57 Blue A
739 181.53 92.39 Grey B
740 177.85 78.93 Green A
741 162.37 80.50 Blue B
742 165.50 98.43 Green B
743 176.27 84.84 Brown B
744 164.03 89.25 Brown B
745 161.26 82.52 Brown B
746 167.59 71.98 Blue B
747 166.67 75.30 Brown B
748 171.85 89.21 Brown B
749 169.35 81.13 Green B
750 164.87 85.42 Green B
751 166.99 71.90 Blue B
752 186.62 62.03 Blue B
753 168.51 76.56 Blue B
754 166.29 77.20 Blue A
755 177.38 91.71 Green B
756 166.82 80.08 Grey B
757 175.70 77.16 Green B
758 172.53 93.36 Brown B
759 170.03 80.04 Blue B
760 166.92 83.79 Blue A
761 162.24 106.70 Blue B
762 159.92 89.30 Grey B
763 173.75 87.83 Grey B
764 168.42 73.74 Green A
765 165.40 89.65 Brown B
766 178.01 57.72 Brown A
767 186.72 97.41 Brown B
768 165.81 79.06 Grey A
769 175.23 84.75 Grey B
770 162.83 74.12 Green B
771 176.22 58.95 Blue B
772 167.14 78.42 Brown B
773 169.12 81.93 Blue A
774 173.01 90.52 Green A
775 168.90 77.67 Blue A
776 166.33 76.26 Blue B
777 176.14 97.18 Brown B
778 154.47 86.45 Blue A
779 166.31 75.06 Grey A
780 171.26 93.70 Brown A
781 165.47 71.88 Grey B
782 163.28 82.55 Blue B
783 178.57 104.71 Green B
784 181.04 91.82 Grey A
785 171.47 68.21 Blue B
786 161.16 75.47 Grey A
787 163.40 94.78 Grey A
788 167.33 58.61 Green B
789 164.35 59.99 Blue B
790 171.62 86.46 Brown A
791 181.28 61.32 Blue B
792 174.92 87.11 Grey A
793 169.18 76.40 Blue A
794 171.77 90.57 Blue B
795 163.38 84.10 Blue B
796 161.01 80.07 Grey A
797 164.67 79.41 Brown A
798 145.77 75.57 Green B
799 168.85 80.74 Brown A
800 178.09 64.67 Blue B
801 166.56 64.92 Green B
802 169.67 62.40 Blue A
803 168.91 75.24 Brown B
804 175.70 86.22 Brown A
805 169.59 75.04 Green A
806 170.56 74.68 Grey B
807 165.75 67.47 Blue A
808 177.28 97.66 Green B
809 166.19 66.06 Brown B
810 161.09 85.11 Brown A
811 175.29 73.76 Blue A
812 167.81 62.30 Blue B
813 149.02 71.32 Brown A
814 175.20 83.20 Brown A
815 162.19 87.18 Grey A
816 162.86 58.45 Blue B
817 174.49 87.36 Grey A
818 166.83 82.74 Grey B
819 168.23 81.04 Green B
820 155.84 85.30 Grey A
821 177.69 72.09 Grey B
822 165.64 64.78 Blue A
823 175.61 57.63 Green A
824 168.65 65.50 Green A
825 168.19 73.50 Brown B
826 160.97 69.17 Brown A
827 172.59 75.15 Grey B
828 164.57 76.37 Grey B
829 161.52 102.10 Blue B
830 167.60 75.63 Green B
831 159.57 82.57 Grey A
832 181.38 67.67 Grey A
833 174.37 83.58 Brown B
834 166.84 101.06 Grey A
835 168.08 78.70 Grey A
836 170.06 84.93 Grey A
837 164.15 81.69 Grey B
838 166.47 79.66 Blue A
839 171.32 93.22 Blue A
840 165.32 61.17 Grey A
841 163.05 90.96 Blue A
842 170.06 82.31 Green B
843 166.00 94.32 Grey B
844 176.88 69.82 Green B
845 171.61 71.17 Green B
846 170.56 77.13 Blue A
847 167.41 71.44 Brown B
848 180.97 70.14 Green A
849 163.05 81.80 Brown A
850 173.24 76.54 Green B
851 171.95 91.83 Grey A
852 172.58 69.53 Grey B
853 169.82 79.90 Grey B
854 168.76 70.36 Brown B
855 165.57 66.94 Brown A
856 165.64 86.68 Grey B
857 172.65 81.79 Grey B
858 174.23 93.83 Grey A
859 170.98 95.12 Green B
860 167.96 100.21 Grey A
861 162.46 73.96 Green A
862 172.17 69.95 Blue B
863 171.55 85.18 Blue B
864 170.75 80.21 Grey B
865 171.45 82.45 Blue A
866 168.86 63.56 Brown A
867 170.94 72.61 Grey B
868 169.32 71.10 Brown A
869 168.43 86.28 Brown B
870 178.98 79.95 Green B
871 162.09 83.66 Green B
872 165.96 79.63 Grey B
873 176.35 91.04 Grey B
874 170.44 77.09 Grey A
875 182.15 62.12 Green A
876 169.59 91.32 Brown B
877 167.78 88.51 Brown B
878 176.23 89.50 Green A
879 175.55 77.28 Blue B
880 174.00 87.61 Grey A
881 171.90 84.87 Grey B
882 171.55 88.03 Grey A
883 175.78 74.56 Green A
884 165.56 95.41 Grey A
885 168.70 83.46 Grey B
886 178.40 79.58 Grey A
887 165.73 63.80 Grey B
888 169.92 69.94 Brown B
889 172.25 87.50 Brown A
890 167.36 83.59 Green B
891 170.87 82.55 Blue A
892 171.85 99.37 Blue A
893 165.09 85.44 Brown A
894 169.12 85.63 Grey B
895 173.59 96.43 Green A
896 166.72 84.92 Brown B
897 167.42 82.32 Blue B
898 175.20 91.37 Green B
899 174.29 72.11 Blue B
900 159.74 82.42 Grey A
901 161.16 94.03 Brown B
902 168.88 77.38 Brown B
903 172.94 84.08 Blue A
904 168.29 66.75 Brown A
905 163.90 96.48 Blue B
906 172.87 76.86 Green B
907 165.00 76.11 Green A
908 176.67 72.49 Brown A
909 173.21 67.43 Blue B
910 178.69 70.71 Grey B
911 175.37 80.74 Blue A
912 170.44 75.34 Brown A
913 183.85 83.16 Grey B
914 165.54 70.05 Brown A
915 165.38 70.01 Brown B
916 174.04 84.48 Grey B
917 176.54 74.08 Blue B
918 166.04 87.86 Blue B
919 183.19 86.52 Blue B
920 176.42 86.11 Blue B
921 168.77 74.25 Grey B
922 169.63 76.10 Green A
923 167.36 95.42 Grey A
924 168.86 87.50 Green B
925 170.80 82.59 Grey B
926 167.38 85.27 Grey B
927 168.57 84.82 Brown A
928 168.52 67.63 Brown B
929 154.96 60.19 Grey A
930 165.01 70.43 Grey B
931 174.22 72.01 Green A
932 163.02 73.59 Brown B
933 168.62 92.42 Blue B
934 170.49 70.01 Green B
935 163.18 72.90 Green A
936 171.04 82.76 Green A
937 177.62 82.10 Grey B
938 177.04 96.87 Grey B
939 168.86 78.12 Grey B
940 170.55 75.40 Brown B
941 166.63 77.53 Brown B
942 174.62 84.61 Brown A
943 169.67 86.01 Grey B
944 173.14 65.30 Brown B
945 168.91 92.88 Grey A
946 175.72 100.47 Blue B
947 168.86 87.00 Blue B
948 163.16 64.77 Green B
949 175.90 96.98 Grey A
950 172.91 82.94 Brown B
951 168.12 83.14 Green A
952 179.05 70.89 Grey B
953 171.53 78.21 Green B
954 166.33 79.46 Brown A
955 167.23 99.24 Green B
956 167.55 70.53 Grey B
957 172.56 77.99 Green B
958 165.40 93.89 Green B
959 167.56 108.18 Brown A
960 179.43 86.27 Grey B
961 168.12 102.66 Green A
962 178.10 81.58 Green B
963 159.26 91.27 Blue A
964 177.55 73.36 Grey A
965 174.34 83.73 Grey A
966 162.21 69.50 Brown A
967 165.94 89.35 Green B
968 175.50 85.62 Green A
969 174.67 66.59 Blue A
970 183.81 72.48 Blue A
971 177.74 71.53 Brown A
972 177.63 83.62 Grey B
973 177.25 89.06 Brown B
974 168.01 77.73 Brown A
975 164.39 87.42 Grey B
976 159.58 83.05 Blue B
977 169.57 90.05 Brown A
978 171.71 72.49 Green A
979 174.01 86.33 Green B
980 169.70 88.73 Brown B
981 171.17 55.67 Grey A
982 183.18 85.62 Blue A
983 167.56 87.83 Green B
984 168.40 72.80 Brown A
985 172.76 64.19 Brown A
986 165.22 79.76 Brown A
987 181.94 81.98 Green B
988 165.45 77.13 Blue A
989 171.64 81.98 Brown A
990 165.18 82.55 Blue A
991 180.16 74.26 Grey A
992 166.35 87.20 Brown A
993 176.88 105.53 Brown B
994 171.26 75.40 Blue B
995 166.23 69.38 Brown B
996 164.65 79.00 Green B
997 163.37 50.55 Green B
998 175.24 63.54 Blue A
999 168.83 72.38 Green A
1000 169.09 76.97 Blue B

How similar are these groups?

Let’s first check their heights:

How similar are these groups?

And their weights:

How similar are these groups?

And their eye colors:

Making sure this wasn’t a fluke

Let’s re-run this:

ID Height Weight Eye colour Group
1 163.78 74.41 Blue A
2 170.58 65.85 Green B
3 166.02 79.59 Grey B
4 171.53 61.86 Brown B
5 172.15 76.90 Blue A
6 164.09 91.73 Green B
7 158.82 80.86 Brown A
8 170.03 91.88 Brown B
9 175.02 77.87 Grey B
10 178.45 90.49 Green A
11 171.41 74.01 Green A
12 168.37 83.30 Blue A
13 168.15 87.85 Blue A
14 166.10 93.43 Brown B
15 171.57 82.85 Blue A
16 161.05 70.65 Grey B
17 160.18 75.65 Blue A
18 159.54 86.05 Brown B
19 161.62 82.55 Brown B
20 165.49 69.62 Grey B
21 167.46 64.25 Blue A
22 166.36 78.28 Green A
23 186.51 84.80 Brown B
24 169.25 83.48 Grey A
25 170.39 98.02 Blue A
26 165.73 82.77 Brown A
27 170.81 79.49 Blue A
28 176.23 93.84 Grey A
29 164.84 92.66 Brown B
30 157.79 78.20 Green A
31 182.74 82.00 Brown A
32 178.83 60.37 Blue B
33 179.13 80.84 Grey A
34 163.60 75.25 Grey A
35 173.66 81.48 Brown B
36 170.36 84.61 Grey B
37 168.86 85.00 Blue B
38 167.28 79.94 Brown B
39 181.19 70.21 Blue B
40 167.24 78.67 Grey B
41 168.28 101.02 Brown B
42 177.86 64.07 Brown A
43 164.96 94.34 Brown A
44 172.15 97.22 Brown B
45 162.56 86.62 Grey B
46 160.63 80.51 Brown B
47 161.30 56.90 Grey A
48 160.91 106.68 Grey B
49 174.49 68.65 Grey A
50 165.60 76.27 Blue A
51 165.26 80.15 Blue A
52 178.85 93.54 Grey A
53 173.52 94.34 Green A
54 172.96 71.86 Blue A
55 172.31 78.71 Grey B
56 157.28 72.91 Brown A
57 160.69 104.73 Blue A
58 173.10 91.82 Grey B
59 170.53 88.23 Grey A
60 172.28 65.95 Green B
61 179.21 80.94 Grey A
62 176.65 77.21 Blue B
63 173.68 81.33 Grey A
64 167.90 81.47 Grey A
65 166.93 86.84 Brown B
66 184.27 69.88 Green B
67 171.05 60.77 Brown A
68 167.49 73.17 Brown A
69 173.77 93.21 Green A
70 166.44 78.07 Grey A
71 170.20 74.07 Blue B
72 166.24 101.94 Green A
73 173.69 76.03 Green B
74 179.62 72.41 Green B
75 172.92 63.11 Grey B
76 172.14 89.46 Green A
77 162.66 72.69 Grey A
78 165.43 75.95 Brown A
79 175.37 86.56 Green B
80 172.78 77.38 Grey A
81 174.25 88.41 Brown A
82 173.25 65.72 Brown B
83 158.99 83.60 Green B
84 174.57 113.29 Brown A
85 162.76 95.24 Brown A
86 161.32 92.46 Grey A
87 171.01 70.59 Green B
88 182.88 69.77 Green B
89 169.70 75.49 Brown B
90 166.00 79.31 Blue A
91 173.04 77.45 Grey B
92 174.02 79.06 Green A
93 165.92 84.13 Brown B
94 177.43 62.88 Brown B
95 175.73 81.72 Brown A
96 178.72 83.87 Grey B
97 161.69 75.05 Green B
98 163.88 64.98 Grey A
99 183.71 76.58 Blue A
100 181.35 84.77 Grey B
101 168.97 85.89 Grey B
102 158.60 104.63 Brown A
103 167.58 94.40 Blue B
104 164.91 77.47 Blue A
105 180.59 66.70 Blue A
106 171.37 80.08 Grey A
107 172.67 72.09 Green B
108 173.79 88.65 Grey B
109 172.12 90.35 Green A
110 177.23 92.71 Grey B
111 162.50 72.28 Grey A
112 164.53 67.57 Blue A
113 167.16 78.42 Blue A
114 171.64 59.48 Green B
115 170.74 81.26 Brown B
116 173.16 71.42 Grey A
117 175.27 73.38 Green A
118 165.88 76.88 Blue B
119 170.11 91.98 Brown B
120 167.81 72.69 Grey B
121 166.64 79.89 Green B
122 173.61 77.53 Grey A
123 165.01 94.00 Green B
124 174.55 85.45 Grey B
125 168.40 86.89 Green B
126 167.79 83.27 Green B
127 181.07 75.26 Blue A
128 178.17 71.25 Green B
129 168.37 82.08 Blue A
130 158.30 77.24 Grey A
131 169.40 82.21 Brown A
132 177.15 77.08 Grey A
133 179.11 89.22 Brown A
134 171.31 79.34 Green A
135 171.05 86.87 Blue A
136 160.21 89.59 Green A
137 180.13 70.70 Green B
138 172.91 86.32 Brown A
139 168.72 85.30 Green A
140 163.08 76.58 Green A
141 165.88 83.30 Brown B
142 170.66 100.31 Grey A
143 169.26 78.26 Grey A
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363 161.92 80.12 Blue B
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365 166.56 80.98 Blue B
366 172.88 70.35 Grey B
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369 154.18 94.37 Brown A
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390 188.86 62.30 Brown A
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417 173.92 72.82 Green B
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419 157.70 73.54 Blue A
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436 167.02 93.03 Grey B
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440 163.83 84.04 Grey B
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460 175.68 80.29 Grey A
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493 182.22 93.15 Blue B
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495 176.07 93.78 Green B
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529 164.18 73.49 Grey A
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547 166.41 69.01 Grey B
548 160.56 80.65 Blue A
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550 171.33 77.58 Blue B
551 164.95 88.68 Green A
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588 162.91 74.58 Blue B
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606 166.35 96.21 Grey B
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668 164.44 83.23 Green A
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703 173.14 84.09 Brown B
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705 165.49 83.35 Blue B
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707 165.08 91.36 Grey A
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710 171.80 64.07 Grey B
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749 169.35 81.13 Green B
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751 166.99 71.90 Blue B
752 186.62 62.03 Blue A
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755 177.38 91.71 Green B
756 166.82 80.08 Grey B
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766 178.01 57.72 Brown B
767 186.72 97.41 Brown B
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769 175.23 84.75 Grey A
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771 176.22 58.95 Blue A
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782 163.28 82.55 Blue A
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785 171.47 68.21 Blue B
786 161.16 75.47 Grey B
787 163.40 94.78 Grey B
788 167.33 58.61 Green B
789 164.35 59.99 Blue B
790 171.62 86.46 Brown B
791 181.28 61.32 Blue A
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795 163.38 84.10 Blue B
796 161.01 80.07 Grey B
797 164.67 79.41 Brown A
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799 168.85 80.74 Brown B
800 178.09 64.67 Blue B
801 166.56 64.92 Green B
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811 175.29 73.76 Blue B
812 167.81 62.30 Blue A
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815 162.19 87.18 Grey B
816 162.86 58.45 Blue A
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818 166.83 82.74 Grey B
819 168.23 81.04 Green B
820 155.84 85.30 Grey B
821 177.69 72.09 Grey B
822 165.64 64.78 Blue A
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824 168.65 65.50 Green A
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830 167.60 75.63 Green B
831 159.57 82.57 Grey A
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833 174.37 83.58 Brown B
834 166.84 101.06 Grey B
835 168.08 78.70 Grey A
836 170.06 84.93 Grey A
837 164.15 81.69 Grey A
838 166.47 79.66 Blue B
839 171.32 93.22 Blue B
840 165.32 61.17 Grey B
841 163.05 90.96 Blue A
842 170.06 82.31 Green B
843 166.00 94.32 Grey A
844 176.88 69.82 Green A
845 171.61 71.17 Green A
846 170.56 77.13 Blue A
847 167.41 71.44 Brown A
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851 171.95 91.83 Grey A
852 172.58 69.53 Grey A
853 169.82 79.90 Grey B
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855 165.57 66.94 Brown A
856 165.64 86.68 Grey A
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858 174.23 93.83 Grey B
859 170.98 95.12 Green A
860 167.96 100.21 Grey B
861 162.46 73.96 Green A
862 172.17 69.95 Blue A
863 171.55 85.18 Blue B
864 170.75 80.21 Grey A
865 171.45 82.45 Blue A
866 168.86 63.56 Brown A
867 170.94 72.61 Grey A
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870 178.98 79.95 Green A
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872 165.96 79.63 Grey B
873 176.35 91.04 Grey B
874 170.44 77.09 Grey A
875 182.15 62.12 Green B
876 169.59 91.32 Brown A
877 167.78 88.51 Brown B
878 176.23 89.50 Green B
879 175.55 77.28 Blue B
880 174.00 87.61 Grey B
881 171.90 84.87 Grey A
882 171.55 88.03 Grey A
883 175.78 74.56 Green A
884 165.56 95.41 Grey A
885 168.70 83.46 Grey B
886 178.40 79.58 Grey B
887 165.73 63.80 Grey B
888 169.92 69.94 Brown B
889 172.25 87.50 Brown B
890 167.36 83.59 Green A
891 170.87 82.55 Blue A
892 171.85 99.37 Blue A
893 165.09 85.44 Brown B
894 169.12 85.63 Grey A
895 173.59 96.43 Green B
896 166.72 84.92 Brown A
897 167.42 82.32 Blue A
898 175.20 91.37 Green A
899 174.29 72.11 Blue B
900 159.74 82.42 Grey B
901 161.16 94.03 Brown A
902 168.88 77.38 Brown B
903 172.94 84.08 Blue A
904 168.29 66.75 Brown A
905 163.90 96.48 Blue B
906 172.87 76.86 Green B
907 165.00 76.11 Green B
908 176.67 72.49 Brown B
909 173.21 67.43 Blue B
910 178.69 70.71 Grey A
911 175.37 80.74 Blue B
912 170.44 75.34 Brown A
913 183.85 83.16 Grey B
914 165.54 70.05 Brown B
915 165.38 70.01 Brown B
916 174.04 84.48 Grey A
917 176.54 74.08 Blue B
918 166.04 87.86 Blue B
919 183.19 86.52 Blue A
920 176.42 86.11 Blue B
921 168.77 74.25 Grey B
922 169.63 76.10 Green B
923 167.36 95.42 Grey B
924 168.86 87.50 Green A
925 170.80 82.59 Grey B
926 167.38 85.27 Grey B
927 168.57 84.82 Brown A
928 168.52 67.63 Brown A
929 154.96 60.19 Grey B
930 165.01 70.43 Grey B
931 174.22 72.01 Green B
932 163.02 73.59 Brown B
933 168.62 92.42 Blue B
934 170.49 70.01 Green B
935 163.18 72.90 Green B
936 171.04 82.76 Green A
937 177.62 82.10 Grey A
938 177.04 96.87 Grey B
939 168.86 78.12 Grey A
940 170.55 75.40 Brown A
941 166.63 77.53 Brown B
942 174.62 84.61 Brown B
943 169.67 86.01 Grey A
944 173.14 65.30 Brown B
945 168.91 92.88 Grey A
946 175.72 100.47 Blue A
947 168.86 87.00 Blue B
948 163.16 64.77 Green A
949 175.90 96.98 Grey B
950 172.91 82.94 Brown B
951 168.12 83.14 Green B
952 179.05 70.89 Grey B
953 171.53 78.21 Green B
954 166.33 79.46 Brown B
955 167.23 99.24 Green A
956 167.55 70.53 Grey B
957 172.56 77.99 Green A
958 165.40 93.89 Green B
959 167.56 108.18 Brown A
960 179.43 86.27 Grey A
961 168.12 102.66 Green B
962 178.10 81.58 Green B
963 159.26 91.27 Blue A
964 177.55 73.36 Grey A
965 174.34 83.73 Grey B
966 162.21 69.50 Brown B
967 165.94 89.35 Green B
968 175.50 85.62 Green A
969 174.67 66.59 Blue B
970 183.81 72.48 Blue B
971 177.74 71.53 Brown A
972 177.63 83.62 Grey B
973 177.25 89.06 Brown A
974 168.01 77.73 Brown B
975 164.39 87.42 Grey B
976 159.58 83.05 Blue B
977 169.57 90.05 Brown A
978 171.71 72.49 Green B
979 174.01 86.33 Green A
980 169.70 88.73 Brown A
981 171.17 55.67 Grey B
982 183.18 85.62 Blue B
983 167.56 87.83 Green A
984 168.40 72.80 Brown A
985 172.76 64.19 Brown B
986 165.22 79.76 Brown A
987 181.94 81.98 Green A
988 165.45 77.13 Blue B
989 171.64 81.98 Brown B
990 165.18 82.55 Blue A
991 180.16 74.26 Grey A
992 166.35 87.20 Brown B
993 176.88 105.53 Brown B
994 171.26 75.40 Blue B
995 166.23 69.38 Brown A
996 164.65 79.00 Green B
997 163.37 50.55 Green B
998 175.24 63.54 Blue B
999 168.83 72.38 Green A
1000 169.09 76.97 Blue A

Check how similar they are

Increasingly similar

In fact, if we did this many, many, many times, these groups would be, on average, increasingly identical!

Why?

  • Central limit theorem

  • Law of large numbers

Do international monitors deter election-day fraud?

Yes!

  • The international community monitored the 2003 Armenian Presidential elections
  • Monitors were assigned randomly to the polling stations
  • Hyde found a big average difference between the vote share received by the cheating party at monitored stations compared to non-monitored stations.